Here is a website that might help explain what happens:
http://www.ehow.com/facts_6072050_effect-garden-plants_-ph-levels.html
You can do some things: simple soil pH test periodically. Adjust as needed with acidifier. I believe you can buy some sort of soil acidifer for azaleas, blueberries, hydrangeas.
You could also plant further in the center of the planter (which I'm sure you would already be doing) instead of near the sides. You could possibly push some plastic or metal (not sure if that would affect soil) panels along the inner brick wall?

There is products such as Drylok that is used on the concrete of watergardens/ fish ponds that seals the effects the lime has on water. This should work for the soil in your raised bed. Hopefully you have enough drainage so any winter freezes won't crack your brick work.